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Lagrange Multipliers
Related Topics
Wize University Calculus 2 Textbook > Multivariable Functions
Max & Min
5 Activities
Practice
Find the maximum and minimum values of
f
(
x
,
y
,
z
)
=
3
x
2
+
y
f(x,~y,~z)=3x^2+y
f
(
x
,
y
,
z
)
=
3
x
2
+
y
subject to
4
x
−
3
y
=
9
and
x
2
+
z
2
=
9
4x-3y=9~\text{and}~x^2+z^2=9
4
x
−
3
y
=
9
and
x
2
+
z
2
=
9
.
Maximum Value =
Minimum Value =
I don't know
Check Submission
More Max & Min Questions:
Practice for classifying critical points
A function
f
(
x
,
y
)
f(x, y)
f
(
x
,
y
)
is found to have the following critical points (listed in the first column). The second derivative test function, D, is defined as:
D
(
x
,
y
)
=
3
x
2
2
y
−
9
x
y
2
x
−
2
y
D(x, y) = \dfrac{3x^22y -9xy}{2x-2y}
D
(
x
,
y
)
=
2
x
−
2
y
3
x
2
2
y
−
9
x
y
and the second derivative with respect to x is given as:
Critical Points
Practice
Find and classify all the critical points for
f
(
x
,
y
)
=
(
y
−
2
)
x
2
−
y
2
f(x,~y)=(y-2)x^2-y^2
f
(
x
,
y
)
=
(
y
−
2
)
x
2
−
y
2
.